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STÜCKELBERG 1953

Stückelberg, E.C.G.; Petermann, A.;
La normalization des constantes dans la theorie des quanta / On the Normalizations of the Quantum Theory Constants
Helv. Phys. Acta 26 (1953) 499;

Summary
This article propose a mathematical foundation to the method previously employed^* to give a definite meaning to the products of invariant distributions such as (⁽¹⁾_x-yD^(s)_x-y + ^(s)(1)), (⁽¹⁾_x-y⁽²⁾_y-zD^(s)_x-z + ... ), etc. in terms of arbitrary constants c₁, c₂ ... c_r(n). The n'th approximation S⁽ⁿ⁾ of the S[V] matrix (defined for a given space time-region V) depends on these r(n) arbitrary constants in addition to the arbitrary physical parameters (masses , , and coupling constants e, g ... ). In the introduction (S 1), we see that a definite physical meaning can be given to the masses , . A coupling parameter, however can only be specified in terms of a chosen development of a function S(xy..,,..,c₁..) of physical significance. However, the terms of the actual correspondence development (in terms of e²) S = S₂ + S₄ + ... have no physical meaning. Therefore the coefficient e² in S₂ has only a mathematical significance. It requires that the functions of xy.. S₂, S₄,..S_n have all be specified. As this specification involves the c_i's, we must expect that a group of infinitesimal operations P_i =(fracpartial partial c_i)_c=o exists, satisfying P_i=h_ie(,,e)fracpartial S(,,e,00...)partial e, admitting thus a renormalization of e.
scriptsize ^* E.C.G.Stückelberg and D.Rivier, E.C.G.Stückelberg and T.A.Green.
( Extracted from the introductory part of the paper.).

Related references
See also
E. C. G. Stückelberg and D. Rivier, Helv. Phys. Acta 23 (1950) 236;
Z. Koba et al., Progr. of Theor. Phys. 6 (1951) 849;
A. Petermann and E. C. G. Stückelberg, Phys. Rev. 82 (1951) 548;
E. C. G. Stückelberg, Phys. Rev. 81 (1951) 130;
E. C. G. Stückelberg, Helv. Phys. Acta 14 (1941) 51;
L. Schwartz, Théorie des distributions. V.I, II Paris (1950, 1951);
E. E. Salpeter and H. A. Bethe, Phys. Rev. 84 (1951) 1232;
R. P. Feynman, Phys. Rev. 76 (1949) 749;
R. P. Feynman, Phys. Rev. 76 (1949) 769;
H. Weyl, Raum-Zeit-Materie 5 ed. Berlin (1951) 128;
L. L. Foldy, Phys. Rev. 84 (1951) 168;
S. N. Gupta, Proc. Phys. Soc. 53 (1950) 681;
K. Bleuler, Helv. Phys. Acta 23 (1950) 567;
H. Fukuda and T. Kinoshita, Progr. of Theor. Phys. 5 (1950) 1024;
A. Salam, Phys. Rev. 82 (1951) 217;
E. C. G. Stückelberg and T. A. Green, Helv. Phys. Acta 24 (1951) 153;